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Implicit Large-Eddy Simulations of Zero-Pressure Gradient, Turbulent Boundary Layer

A set of direct simulations of zero-pressure gradient, turbulent boundary layer flows are conducted using various span widths (62-630 wall units), to document their influence on the generated turbulence. The FDL3DI code that solves compressible Navier-Stokes equations using high-order compact-difference scheme and filter, with the standard recycling/rescaling method of turbulence generation, is used. Results are analyzed at two different Re values (500 and 1,400), and compared with spectral DNS data. They show that a minimum span width is required for the mere initiation of numerical turbulence. Narrower domains ((is) less than 100 w.u.) result in relaminarization. Wider spans ((is) greater than 600 w.u.) are required for the turbulent statistics to match reference DNS. The upper-wall boundary condition for this setup spawns marginal deviations in the mean velocity and Reynolds stress profiles, particularly in the buffer region.

Turblent boundary layer↗

Large Eddy Simulation of a Film Cooling Flow Injected from an Inclined Discrete Cylindrical Hole into a Crossflow with Zero-Pressure Gradient Turbulent Boundary Layer

A Large Eddy Simulation (LES) is performed of a high blowing ratio (M = 1.7) film cooling flow with density ratio of unity. Mean results are compared with experimental data to show the degree of fidelity achieved in the simulation. While the trends in the LES prediction are a noticeable improvement over Reynolds-Averaged Navier-Stokes (RANS) predictions, there is still a lack a spreading on the underside of the lifted jet. This is likely due to the inability of the LES to capture the full range of influential eddies on the underside of the jet due to their smaller structure. The unsteady structures in the turbulent coolant jet are also explored and related to turbulent mixing characteristics

Johnson, Perry L.↗

Prediction of Transitional Flows in the Low Pressure Turbine

Current turbulence models tend to give too early and too short a length of flow transition to turbulence, and hence fail to predict flow separation induced by the adverse pressure gradients and streamline flow curvatures. Our discussion will focus on the development and validation of transition models. The baseline data for model comparisons are the T3 series, which include a range of free-stream turbulence intensity and cover zero-pressure gradient to aft-loaded turbine pressure gradient flows. The method will be based on the conditioned N-S equations and a transport equation for the intermittency factor. First, several of the most popular 2-equation models in predicting flow transition are examined: k-e [Launder-Sharina], k-w [Wilcox], Lien-Leschiziner and SST [Menter] models. All models fail to predict the onset and the length of transition, even for the simplest flat plate with zero-pressure gradient(T3A). Although the predicted onset position of transition can be varied by providing different inlet turbulent energy dissipation rates, the appropriate inlet conditions for turbulence quantities should be adjusted to match the decay of the free-stream turbulence. Arguably, one may adjust the low-Reynolds-number part of the model to predict transition. This approach has so far not been very successful. However, we have found that the low-Reynolds-number model of Launder and Sharma [1974], which is an improved version of Jones and Launder [1972] gave the best overall performance. The Launder and Sharma model was designed to capture flow re-laminarization (a reverse of flow transition), but tends to give rise to a too early and too fast transition in comparison with the physical transition. The three test cases were for flows with zero pressure gradient but with different free-stream turbulent intensities. The same can be said about the model when considering flows subject to pressure gradient(T3C1). To capture the effects of transition using existing turbulence models, one approach is to make use of the concept of the intermittency to predict the flow transition. It was originally based on the intermittency distribution of Narasimha [1957], and then gradually evolved into a transport equation for the intermittency factor. Gostelow and associates [1994,1995] have made some improvements to Narasimha's method in an attempt to account for both favorable and adverse pressure gradients. Their approach is based on a linear, explicit combination of laminar and turbulent solutions. This approach fails to predict the overshoot of the skin friction on a flat plate near the end of transition zone, even though the length of transition is well predicted. The major flaw of Gostelow's approach is that it assumes the non-turbulent part being the laminar solution and the turbulent part being the turbulent solution and they do not interact across the transitional region. The technique in condition averaging the flow equations in intermittent flows was first introduced by Libby [1975] and Dopazo [1977] and further refined by Dick and associates [1988, 1996]. This approach employs two sets of transport equations for the non-turbulent part and the other for the turbulent part. The advantage of this approach is that it allows the interaction of non-turbulent and turbulent velocities through the introduction of additional source terms in the continuity and momentum equations for the non-turbulent and turbulent velocities. However, the strong coupling of the two sets of equations has caused some numerical difficulties, which requires special attention. The prediction of the skin friction can be improved by this approach via the implicit coupling of non-turbulent and turbulent velocity flelds. Another improvement of the interrmittency model can be further made by allowing the intermittency to vary in the cross-stream direction. This is one step prior to testing any proposal for the transport equation for the intermittency factor. Instead of solving the transport equation for the intermittency factor, the distribution for the intermittency factor is prescribed by Klebanoff's empirical formula [1955]. The skin friction is very well predicted by this new modification, including the overshoot of the profile near the end of the transition zone. The outcome of this study is very encouraging since it indicates that the proper description of the intermittency distribution is the key to the success of the model prediction. This study will be used to guide us on the modelling of the intermittency transport equation.

Huang, George↗

Effect of Pressure Gradients on Plate Response and Radiation in a Supersonic Turbulent Boundary Layer

Using the model developed by the author for zero-pressure gradient turbulent boundary layers, results are obtained for adverse and favorable pressure gradients. It is shown that when a flexible plate is located in an adverse pressure gradient area, it vibrates more than if it were in a favorable pressure gradient one. Therefore the noise generated by the plate in an adverse pressure gradient is much greater than that due to the plate in a favorable pressure gradient. The effects of Reynolds number and boundary layer thickness are also analyzed and found to have the same effect in both adverse and favorable pressure gradient cases. Increasing the Reynolds number is found to increase the loading on the plate and therefore acoustic radiation. An increase in boundary layer thickness is found to decrease the level of the high frequencies and therefore the response and radiation at these frequencies. The results are in good qualitative agreement with experimental measurements.

Frendi, Abdelkader↗

Experimental Evaluation of an Isolated Synthetic Jet IN Crossflow

The second case for this workshop builds upon the isolated synthetic jet of Case 1 by adding a crossflow, with no streamwise pressure gradient, for the developing jet to interact with. Formally, Case 2 examines the interaction of a single, isolated, synthetic jet and a fully turbulent zero-pressure gradient boundary layer. The resulting flow has many of the characteristics that need to be modeled with fidelity if the results of the calculations are to serve as the basis for research and design with active flow control devices. These include the turbulence in the boundary layer, the time-evolution of the large vortical structure emanating from the jet orifice and its subsequent interaction with and distortion by the boundary layer turbulence, and the effect of the suction cycle on the boundary layer flow. In a synthetic jet, the flow through the orifice and out into the outer flowfield alternates between an exhaust and a suction cycle, driven by the contraction and expansion of a cavity internal to the actuator. In the present experiment, the volume changes in the internal cavity are accomplished by replacing one of the rigid walls of the cavity, the wall opposite the orifice exit, with a deformable wall. This flexible wall is driven by a bottom-mounted moveable piston. The piston is driven electro-mechanically. The synthetic jet issues into the external flow through a circular orifice. In the present experiment, this orifice has a diameter of 0.250 inches (6.35 mm). The flow is conceptually similar to that documented in Schaeffler [1]. To document the flow, several measurement techniques were utilized. The upstream boundary conditions (in-flow conditions), and several key phase-averaged velocity profiles were measured with a 3-component laser-Doppler velocimetry system. Phase-averaged velocity field measurements were made with both stereo digital particle image velocimetry and 2-D digital particle image velocimetry as the primary measurement system. Surface pressure measurements were made utilizing an electronically scanned pressure system.

Schaeffler, Norman W.↗

Roughness induced transition criteria for space shuttle-type vehicles

Tripping effectiveness of surface roughness on a delta wing shuttle orbiter model at 20 deg angle of attack is compared to that on plane and axisymmetrical bodies with and without longitudinal pressure gradients. The experimental data presented are compared on the basis of effective roughness Reynolds number since this parameter is not sensitive to flow conditions downstream of the roughness. The discussion covers the effective roughness Reynolds number as a function of roughness position Reynolds number, effective size ratio as a function of pressure gradient and distance from vehicle nose, and effect of spanwise roughness position on roughness effectiveness. It is shown that conventional criteria for sizing roughness elements which promote transition in two-dimensional zero-pressure gradient flows are insufficient for high-pressure gradient flows and three-dimensional flows. Roughness much smaller than that given by conventional criteria can cause transition and significantly increase the heating load.

Morrisette, E. L.↗

Theory of instability and transition

The strongly nonlinear area of theory is discussed, as well as linear and weakly nonlinear (i.e., perturbation) theories, and it is noted that the weaknesses of the weakly nonlinear theory are essentially the inappropriate formulation in earlier works and the lack of guidance for the choice of the lowest-order basis. Attention is focused on the areas of theoretical/numerical development contributing to understanding the transition mechanism and new means for analyzing and predicting transition quantitatively. The nonlinear stability of nonparallel flows, linear secondary instability, and nonlinear wave interaction are analyzed. The incompressible flow over a flat plate with zero-pressure gradient is chosen as an example, while applications range to other shear flows including three-dimensional and compressible boundary layers.

Herbert, Thorwald↗

A High-Lift Building Block Flow: Turbulent Boundary Layer Relaminarization

A working wind tunnel test facility has been constructed at the University of Notre Dame's Hessert Center. The relaminarization test facility has been constructed in the 1.5m x 1.5m (5ft x 5 ft) atmospheric wind tunnel and generates a Re(theta)=4694 turbulent boundary layer in nominally zero-pressure gradient before it is exposed to the Case #1 pressure gradient (K approximately equal to 4.2 x 10(exp -6), which is believed to be sufficient to achieve relaminarization. Future work to be conducted will include measuring the response of the turbulent boundary layer to the favorable pressure gradients created in the test facility and documenting this response in order to understand the underlying flow physics responsible for relaminarization. It is the goal of this research to have a better understanding of accelerated turbulent boundary layers which will aid in the development of future flow diagnostic utilities to be implemented in applied aerodynamic research.

Bourassa, Corey↗

Effects of Riblets on Skin Friction in High-Speed Turbulent Boundary Layers

Direct numerical simulations of spatially developing turbulent boundary layers over riblets are conducted to examine the effects of riblets on skin friction at supersonic speeds. Zero-pressure gradient boundary layers with an adiabatic wall, a Mach number of M1 = 2.5, and a Reynolds number based on momentum thickness of Re = 1720 are considered. Simulations are conducted for boundary-layer flows over a clean surface and symmetric V- groove riblets with nominal spacings of 20 and 40 wall units. The DNS results confirm the few existing experimental observations and show that a drag reduction of approximately 7% is achieved for riblets with proper spacing. The influence of riblets on turbulence statistics is analyzed in detail with an emphasis on identifying the differences, if any, between the drag reduction mechanisms for incompressible and high-speed boundary layers.

Duan, Lian↗

Direct Numerical Simulations of High-Speed Turbulent Boundary Layers over Riblets

Direct numerical simulations (DNS) of spatially developing turbulent boundary layers over riblets with a broad range of riblet spacings are conducted to investigate the effects of riblets on skin friction at high speeds. Zero-pressure gradient boundary layers under two flow conditions (Mach 2:5 with T(sub w)/T(sub r) = 1 and Mach 7:2 with T(sub w)/T(sub r) = 0:5) are considered. The DNS results show that the drag-reduction curve (delta C(sub f)/C(sub f) vs l(sup +)(sub g )) at both supersonic speeds follows the trend of low-speed data and consists of a `viscous' regime for small riblet size, a `breakdown' regime with optimal drag reduction, and a `drag-increasing' regime for larger riblet sizes. At l l(sup +)(sub g) approx. 10 (corresponding to s+ approx 20 for the current triangular riblets), drag reduction of approximately 7% is achieved at both Mach numbers, and con rms the observations of the few existing experiments under supersonic conditions. The Mach- number dependence of the drag-reduction curve occurs for riblet sizes that are larger than the optimal size, with smaller slopes of (delta C(sub f)/C(sub f) for larger freestream Mach numbers. The Reynolds analogy holds with 2(C(sub h)=C(sub f) approximately equal to that of at plates for both drag-reducing and drag-increasing configurations.

Duan, Lian↗

Improved Convergence and Robustness of USM3D Solutions on Mixed Element Grids (Invited)

Several improvements to the mixed-element USM3D discretization and defect-correction schemes have been made. A new methodology for nonlinear iterations, called the Hierarchical Adaptive Nonlinear Iteration Scheme (HANIS), has been developed and implemented. It provides two additional hierarchies around a simple and approximate preconditioner of USM3D. The hierarchies are a matrix-free linear solver for the exact linearization of Reynolds-averaged Navier Stokes (RANS) equations and a nonlinear control of the solution update. Two variants of the new methodology are assessed on four benchmark cases, namely, a zero-pressure gradient flat plate, a bump-in-channel configuration, the NACA 0012 airfoil, and a NASA Common Research Model configuration. The new methodology provides a convergence acceleration factor of 1.4 to 13 over the baseline solver technology.

Pandya, Mohagna J.↗

Numerical Investigation of the Effect of Trailing Edge Thickness of Simulated CMC Blades on Loss Profiles

To understand such an aerodynamic characteristic of the CMC blades, we numerically simulated three different CMC blades with varying trailing edge thicknesses. We utilized both Large Eddy simulation (LES) with the dynamic subgrid closure as well a recently implemented Reynolds-averaged Navier-Stokes (RANS) coupled with an intermittency function-based transition model. We considered two sets of experimental test points with different Reynolds numbers at a given high-free stream turbulence range (Tu=~10-13%). The LES was previously validated by comparing with experimental data. We validated the RANS transition model against the ERCOFTAC experimental zero-pressure gradient smooth flat plate boundary layer at low- and high freestream turbulence offered by the experimental data of the Stripf’s for a turbine blade. We confirmed that the predicted skin friction and the heat flux agree well with the data. Finally, we computed the predicted pressure loading profiles, total loss distributions, and integrated loss of the three different CMC blades and made comparisons against the experimental data acquired at NASA Glenn Transonic Turbine Blade Cascade Rig. Our paper will present the aforementioned results and discuss the ability of LES and RANS model of our choice to predict salient aerodynamic characteristics of the blades with the various trailing edge thickness effects.

LES↗

Numerical Investigation of the Effect of Trailing Edge Thickness of Simulated CMC Blades on Loss Profiles

To understand such an aerodynamic characteristic of the CMC blades, we numerically simulated three different CMC blades with varying trailing edge thicknesses. We utilized both Large Eddy simulation (LES) with the dynamic subgrid closure as well a recently implemented Reynolds-averaged Navier-Stokes (RANS) coupled with an intermittency function-based transition model. We considered two sets of experimental test points with different Reynolds numbers at a given high-free stream turbulence range (Tu=~10-13%). The LES was previously validated by comparing with experimental data. We validated the RANS transition model against the ERCOFTAC experimental zero-pressure gradient smooth flat plate boundary layer at low- and high freestream turbulence offered by the experimental data of the Stripf’s for a turbine blade. We confirmed that the predicted skin friction and the heat flux agree well with the data. Finally, we computed the predicted pressure loading profiles, total loss distributions, and integrated loss of the three different CMC blades and made comparisons against the experimental data acquired at NASA Glenn Transonic Turbine Blade Cascade Rig. Our paper will present the aforementioned results and discuss the ability of LES and RANS model of our choice to predict salient aerodynamic characteristics of the blades with the various trailing edge thickness effects.

LES↗

Photophoretic Propulsion Enabling Mesosphere Exploration NIAC Phase I Final Report

This Phase I report presents a comprehensive study on photophoretic flyers—innovative, ultralight, solar-powered vehicles that harness photophoretic forces generated via Knudsen pumping to achieve sustained flight in the mesosphere (50–80 km altitude). By integrating advanced materials such as nanocardboard— characterized by its extremely low areal density (~1 g/m²) and high bending stiffness—with ultrathin light-absorbing coatings, the project converts incident solar radiation directly into a directed thrust. Extensive experimental investigations, coupled with high-fidelity computational fluid dynamics (CFD) simulations using ANSYS Fluent, validate the concept across various three-dimensional geometries, including spherical, conical, and rocket-shaped configurations. These simulations bridge the gap between free-molecular and continuum flow regimes, demonstrating that optimized designs can generate lift forces sufficient to support kilogram-scale payloads even in low-pressure environments. At the heart of this innovation is the use of Knudsen pumping, where temperature gradients across porous surfaces induce directional gas flow, creating a modest overpressure that provides lift. The report introduces an analytical framework that interpolates between the well-known low-Reynolds number drag regime and the high-Reynolds number momentum theory. This model accurately predicts lift based on design parameters such as microchannel dimensions, porous wall geometry, areal density, and nozzle exit area. For instance, simulations indicate that 10-meter-scale structures with carefully engineered porous walls can achieve the necessary pressure differential to support scientifically significant payloads (~1 kg). The study also explores a hybrid propulsion approach that combines solar buoyancy with photophoretic lift. Initially, solar heating creates a buoyant force that elevates the flyer to mesospheric altitudes. Once in the optimal pressure range, the photophoretic mechanism—powered by Knudsen pumping—takes over as the primary source of lift, ensuring stable, long-duration flight. This dual-mode operation not only facilitates the deployment of photophoretic flyers but also broadens the potential applications for mesospheric exploration. In addition to propulsion, the report investigates the integration of photophoretic thrusters for trajectory control of existing research balloons in the upper stratosphere. By dynamically adjusting the nozzle orientation and controlling the flow-through velocity, these thrusters provide precise maneuverability, enabling the flyers to counteract atmospheric disturbances and adjust their flight paths in real time. For example, a photophoretic thruster approximately 7.5 by 7.5 meters in size could be unfolded below a payload gondola of a 60 million-cubic-foot zero-pressure balloon. Such a thruster can provide horizontal speed control of approximately 1 m/s using only sunlight and no moving parts (except those needed to track the Sun and control the jet direction). Importantly, photophoretic thrusters operate more efficiently at higher altitudes, which is complementary to known trajectory control techniques, such as propellers and tethered wings, which are more effective at lower altitudes. Finally, the report identifies three scientific research thrusts where mesospheric aircraft technology can have a profound impact: atmospheric tides, characterization of gravity waves, and investigation of mesospheric instabilities. Overall, the findings of this Phase I project represent a significant advancement in photophoretic propulsion technology. By demonstrating that large-scale, ultralight structures can be powered solely by solar radiation—via carefully engineered Knudsen pumping—this work lays a robust foundation for scalable, near-space flight architectures. Future refinements in material fabrication, structural optimization, and integrated trajectory control are expected to further enhance performance, paving the way for operational demonstrations that could revolutionize atmospheric science, remote sensing, and communication networks.

Knudsen Pump↗